JAMB 2013 Mathematics · Question 47

In how many ways can a student select 2 subjects from 5 subjects?

Options

A. $\frac{5!}{3!}$
B. $\frac{5!}{2!2!}$
C. $\frac{5!}{2!3!}$
D. $\frac{5!}{2!}$

Answer: C. $\frac{5!}{2!3!}$

Explanation written with AI and checked against the answer key

1. Analyze the question

The question asks for the number of ways to select 2 subjects out of 5. In mathematics, when we are selecting items where the order of selection does not matter (e.g., choosing Mathematics and Physics is the same as choosing Physics and Mathematics), we use the concept of Combinations.

2. Explain the concept

The formula for combinations is denoted as $^nC_r$ , which represents selecting $r$ items from a total of $n$ items. The formula is:

^nC_r = \frac{n!}{r!(n - r)!}

Where:

$n$ = total number of items (5 subjects)
$r$ = number of items to be selected (2 subjects)
$!$ = factorial (e.g., $5! = 5 \times 4 \times 3 \times 2 \times 1$ )

3. Show the solution

Given $n = 5$ and $r = 2$ :

Substitute these values into the combination formula:

^5C_2 = \frac{5!}{2!(5 - 2)!}

Simplify the expression in the denominator:

^5C_2 = \frac{5!}{2! \times 3!}

Comparing this result to the provided options, we can see that it matches option C.

4. Identify the answer

The expression $\frac{5!}{2!3!}$ correctly represents the number of ways to choose 2 subjects from 5.

Correct Option: C

5. Tip

Whenever you see "selecting" or "choosing" a group from a larger set where the order doesn't matter, always think Combination. A quick way to remember the formula is: "Total factorial divided by (Selected factorial times Remaining factorial)."

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